Oriented vehicles travelling in spherical space

Holderbaum, William and Biggs, J.D.
(2009)
Oriented vehicles travelling in spherical space.
In: The 11th IASTED International Conference on Control and its Applications, 2009-07-13 - 2009-07-15, Cambridge, UK.

Abstract

This paper tackles the path planning problem for oriented vehicles travelling in the non-Euclidean 3-Dimensional space; spherical space S3 . For such problem the orientation of the vehicle is naturally represented by orthonormal frame bundle; the rotation group SO(4). Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to control systems deﬁned on Lie groups. The oriented vehicles, in this case, are constrained to travel at constant speed in a forward direction and their angular velocities directly controlled. In this paper we identify controls that induce steady motions of these oriented vehicles and yield closed form parametric expressions for these motions. The paths these vehicles trace are deﬁned explicitly in terms of the controls and therefore invariant with respect to the coordinate system used to describe the motion.